Question

PLEASE HELP ME

Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. (4 points) Show your work.

For some reason the picture changed when I uploaded it but

A is (2x + 3)

B doesn't have a answer because we're supposed to find that

C is (2x + 1)

D is is the same as the picture which is (x - 10)

Answer 1

The measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°

Step-by-step explanation:

Given that the quadrilateral ABCD is inscribed in a circle.

The given angles are ∠A = (2x + 3), ∠C = (2x + 1) and ∠D = (x - 10)

We need to determine the measures of the angles A, C and D

The value of x:

We know that, the opposite angles of a cyclic quadrilateral add up to 180°

Thus, we have,

`\angle A+\angle C=180^(\circ)`

Substituting the values, we have,

`2x+3+2x+1=180`

`4x+4=180`

`4x=176`

`x=44`

Thus, the value of x is 44.

Measure of ∠A:

Substituting
`x=44` in ∠A = (2x + 3)°, we get,

`\angle A=(2(44)+3)^(\circ)`

`=(88+3)^(\circ)`

`\angle A=91^(\circ)`

Thus, the measure of angle A is 91°.

Measure of ∠C :

Substituting
`x=44` in ∠C = (2x + 1)°, we get,

`\angle C=(2(44)+1)^(\circ)`

`=(88+1)^(\circ)`

`\angle C=89^(\circ)`

Thus, the measure of angle C is 89°.

Measure of ∠D :

Substituting
`x=44` in ∠D = (x - 10)°, we get,

`\angle D=(44-10)^(\circ)`

`\angle D=34^(\circ)`

Thus, the measure of angle D is 34°.

Hence, the measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°